Water flows at a rate of 5 km/h through a pipe of radius 7 cm into a rectangular tank of length 100 m and breadth 88 m. The time (in hours) in which the level of water in the tank will rise by 14 cm is (take π = 22/7): 

Given:

Water flow rate = 5 km/h = 5000 m/h

Radius of pipe = 7 cm = 0.07 m

Length of tank = 100 m

Breadth of tank = 88 m

Rise in water level = 14 cm = 0.14 m

Formula Used:

Volume of water flowing per unit time from pipe = Area of pipe cross-section × Speed of water

Area of pipe cross-section = \(\pi r^2\)

Volume of water in tank = Length × Breadth × Height

Time = Total Volume required / Volume flow rate

Calculation:

Volume of water flowing through the pipe per hour:

Volume flow rate (V_pipe) = \(\pi r^2 \times \text{speed}\)

V_pipe = \(\frac{22}{7} \times (0.07)^2 \times 5000\)

V_pipe = \(\frac{22}{7} \times 0.0049 \times 5000\)

V_pipe = \(22 \times 0.0007 \times 5000\)

V_pipe = 22 × 3.5

⇒ V_pipe = 77 m³/hour

Required volume in tank (V_tank) = L × B × H

V_tank = 100 m × 88 m × 0.14 m

V_tank = 8800 × 0.14

⇒ V_tank = 1232 m³

Time = \(\frac{\text{Required volume in tank}}{\text{Volume flow rate from pipe}}\)

Time = \(\frac{1232 \text{ m}^3}{77 \text{ m}^3/\text{hour}}\)

⇒ Time = 16 hours

∴ The time in which the level of water in the tank will rise by 14 cm is 16 hours.